1)
When did this war occur?
1.
Malbim citing Mahari: It was towards the end of David's life, after Avshalom's rebellion. After this he had Shalom and he found the place for the Mikdash, like the Navi predicted. 1
1
It says (7:10) that after Hashem will give a place for Yisrael (i.e. the Beis ha'Mikdash - Radak there, citing Tanchuma Terumah 9) "v'Lo Yirgaz Od."
2)
Why did David become weary?
1.
Malbim: He was old and weak.
